Final answer:
The work required to stretch a spring 3 inches beyond its natural length is 0.9375 ft-lb, which can be calculated using the work formula W = ½kx² and considering that work is proportional to the square of the displacement.
Step-by-step explanation:
The amount of work required to stretch or compress a spring is given by the formula W = (1/2)kx², where W is the work, k is the spring constant, and x is the displacement from the spring's equilibrium position. Since it is given that stretching the spring 1 ft (or 12 inches) requires 15 ft-lb of work, you can determine the work needed to stretch it by any other distance by adjusting the displacement in the formula accordingly. For stretching the spring by 3 inches (1/4 of the original distance), the work required would be 1/16 of the work needed for stretching it 1 ft, since work is proportional to the square of the displacement.
Calculation: Original work for 1 ft (12 inches) is 15 ft-lb. For 3 inches, which is 1/4 of 12 inches:
W = 15 ft-lb × (3 inches / 12 inches)²
W = 15 ft-lb × (1/4)²
W = 15 ft-lb × 1/16
W = 15/16 ft-lb
W = 0.9375 ft-lb
Therefore, stretching the spring 3 inches beyond its natural length requires 0.9375 ft-lb of work.